1. Field of the Invention
This invention relates to the field of petroleum and ground water engineering. More specifically, it relates to testing of wells in porous formations, including oil wells, gas wells and water wells of all types.
2. Description of the Prior Art
U.S. Pat. Nos. 4,783,769 and 4,802,144, both Holzhausen et al., disclose the use of pressure and flow oscillations for evaluation of the geometry of open fractures and other open fluid-filled conduits intersected by a well bore. These documents do not disclose methods for obtaining properties of porous formations or granular materials. U.S. Pat. No. 4,802,144 discloses a method and apparatus otherwise in several respects analogous to that of the present invention.
U.S. Pat. No. 4,779,200, Bradbury et al., describes a method wherein pressure oscillations are initiated downhole using a drill stem testing (DST) apparatus. These oscillations are then used to evaluate the porosity, permeability or the porosity-permeability product of the subsurface formation adjacent to the DST device.
Bradbury et al. require that the DST device, complete with packer, downhole valve, downhole pressure transducer and downhole flow meter, be lowered on drill pipe to the formation to be tested. This costly requirement limits the usefulness of the invention. Bradbury et al. partially fill a drill pipe with a column of liquid. Bradbury et al. measure pressure downhole only at the DST device and not at the well head, and not at a plurality of points in the well Bradbury et al. also disadvantageously provide a methodology for determining permeability and/or porosity only.
The method of Bradbury et al. investigates only the zone packed off by the DST device. Bradbury et al. interpret only the fundamental frequency of oscillations in the drill pipe. This approach ignores the valuable information contained in higher-frequency oscillations.
U.S. Pat. Nos. 4,783,769 and 4,802,144 disclose the use of inertial effects in interpreting pressure oscillations in well bores intersected by open conduits such as open hydraulic fractures. General mathematical descriptions of wave propagation in fluid-filled pipes are also found in the textbooks of E. B. Wiley and V. L. Streeter, Fluid Transients, (FEB Press, 1982) and John Parmakian, Waterhammer Analysis, (Dover Publications 1963).
From the above cited sources, it is known that the equation for dynamic force equilibrium in the fluid in the well can be written as: ##EQU1## The equation for continuity in the fluid system can be written as: ##EQU2## where V is particle velocity in the fluid, H hydrostatic head, t time, z distance parallel to the axis of the well, a wavespeed in the fluid and g gravitational acceleration.